Heteroscedastic Deep Ensemble for 1D Advection-Diffusion-Reaction¶

Notebook: HeteroscedasticDeepEnsemble_AdvectionDiffusionReaction1D_Tutorial.ipynb

This tutorial extends the 1D ADR problem with spatially varying observation noise. Each ensemble member predicts both a mean response and a local noise variance, allowing the notebook to separate epistemic and aleatoric uncertainty.

Key ideas: - heteroscedastic Gaussian outputs, - aleatoric noise highest near the center of the domain, - ensemble spread vs predicted noise comparison.

Primary references: - Nix, Weigend (1994), Estimating the Mean and Variance of the Target Probability Distribution. DOI: 10.1109/ICNN.1994.374138 - Kendall, Gal (2017), What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision? NeurIPS proceedings - Lakshminarayanan, Pritzel, Blundell (2017), Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles. NeurIPS proceedings